The invention is based on a fuel injection system for internal combustion engines with multiple valves. A fuel injection system with electromagnetic valve actuation is alreaady known, in which the injection valves are connected flush with a common, horizontally disposed fuel manifold distributor. It has the disadvantage, however, that when switching off the warmed-up internal combustion engine, vapor lock bubbles are formed in the injection valves and the fuel lines. When the internal combustion engine is started up once again, said vapor lock bubbles are transported to the injection valves, where sputtering and spark failure occur, and eventually engine failure as well.